In mathematics, a pointed set is a set with a distinguished element, which is called the basepoint. Maps of pointed sets (based maps) are those functions that map one basepoint to another, i.e. a map such that . This is usually denoted
- .
Pointed sets may be regarded as a rather simple algebraic structure. In the sense of universal algebra, they are structures with a single nullary operation which picks out the basepoint.
The class of all pointed sets together with the class of all based maps form a category.
A pointed set may be seen as a pointed space under the discrete topology or as a vector space over the field with one element.
Famous quotes containing the words pointed and/or set:
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Choose thou, before that spirit die,
A piercing pain, a killing sin,
And to my dead heart run them in!”
—Robert Louis Stevenson (1850–1894)
“The monotonous dead clog me up and there is only
black done in black that oozes from the strongbox.
I must disembowel it and then set the heart, the legs,
of two who were one upon a large woodpile
and ignite, as I was once ignited, and let it whirl
into flame....”
—Anne Sexton (1928–1974)